76 Proceedmgs of tJie Royal Society of Victoria. 



The fourth equation, being quadratic, yields two values, the 

 lesser one applying to the tirst and the larger one to the fourth 

 member of the series. 



The value of 7i may also be found by approximation, viz., by 

 substituting successively probable values for n into equation 

 No. 3, until the most satisfactory results are obtained. Both 

 methods may be employed, the first when the experimental data 

 are very correct, the latter in doubtful cases. 



The values of n, x, y and z, determined from the experimental 

 data for the alkalies and Helium, are contained in the table of 

 spectral constants given below, from the study of which the 

 following results have been derived. 



Calling X the root and n the modulus, and denoting the 

 principal series by a, «' and d\ the subordinate series by b, b^, Ir- 

 and c, c^, r, I have arrived at the propositions : — ■ 



1. Each element has two roots for its four subordinate series, 

 and two, possibly only one, for its two head or principal series. 



2. The modulus of the subordinate series b, b^, IP- is a round 

 number, of the coordinate series <:, c^, c a fractional value. 



I propose to call the series b^ /^\ F~ the normal, the series c, c^, r 

 the abnormal one. 



3. The atomic weights are directly proportional to the square 

 I'oots of the difference of the roots (.v) of the subordinate series. 



In the following little table the first line contains the difference 

 of tlie roots of the subordinate series for each element ; the 

 second, the square roots of these numbers ; the third, the atomic 

 weights, and the fourth, the atomic weights divided by the 

 square roots. 



Helium. Li. Na. K. Rb. Cs. 



The constancy of the last line for the alkalies proves the 

 proposition. 



Whether the two head series start from a single root or not is 

 a point I have, so far, not been able to settle. The data to hand 

 are not sufiiciently precise, or the series too short. The modulus 

 advances in value with the atomic weight, viz.. Helium = -94 ; 



